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Denominator is a divisor factor. The denominator is the bottom number of fractions. In simpler terms, it is a number that is below the horizontal line in fractions. A Denominator cannot be equal to 0. It shows the total number of equal parts the numerator is divided into. In this article, we will discuss the Denominator, and numerator, their properties, and more.
What is a Denominator?
A Denominator is a bottom part of a fraction. The denominator shows the total number of parts that sum up to form the whole of the numerator.
A fraction is identified by a horizontal bar. It is identified between two numbers. This bar is known as a fractional bar. The number on the top is known as a numerator. The number below is known as a Denominator.
Fractions: Numerator and Denominator
In a fraction, the denominator and numerator play distinct roles:
Denominator: The denominator indicates the total number of equal parts that make up a whole. It represents how many parts the unit or whole is divided into.
Numerator: The numerator indicates how many parts are selected from the total number of equal parts represented by the denominator.
For example:
In the fraction 4/6, the numerator 4 represents 4 equal parts. The Denominator 6 represents the 6 equal parts that make up the whole.
Types of Fractions
- Proper Fractions: The numerator is smaller than the denominator (for example: 3/5).
- Improper Fractions: The numerator is greater than or equal to the denominator (for example: 9/5).
- Mixed Numbers: A whole number combined with a proper fraction (for example: 2×3/5).
- Like Fractions: Fractions with the same denominator (for example: 3/5 and 9/5).
- Unlike Fractions: Fractions with different denominators (for example: 3/5 and 9/11).
- Equivalent Fractions: Different fractions that represent the same value (for example: 3/2 and 9/6).
Examples of Denominator
Examples of denominators are very simple. In the fraction a/b, a is the numerator and b is the Denominator. Various numbers are also expressed in the same way like x/y, a/b, c/d, where x, a, c are the numerator and y, b, d are denominators.
Imagine a circular shape divided into 6 equal parts, where 4 of those parts are shaded. The shaded portions visually represent the fraction 4/6, showing that 4 parts (numerator) out of the total 6 parts (denominator) are chosen.
What is a Common Denominator
If Denominators of two or more fractions are the same then they are known as the common Denominator. They are also known as like and unlike fractions. The least common denominator is the smallest number. A Common Denominator gives a set of fractions. In arithmetic operations such as Addition and subtraction the fractions are common or equal, it becomes easy to add or subtract them.
Addition and Subtraction of Fractions
Addition and subtraction can compare two or more fractions and it is only possible when fractions have a common Denominator.
For example, if you need to add 4/12 and 2/12, then we can easily add them. We know that their denominators are the same. Therefore, the result will be 4/12 + 2/12 = 6/12 = 1/2 = 0.5
But what about the fractions that have different denominators? For example 2/7 , 9/11 ,and 4/9. To solve these sorts of fractions, we use the concept of the Least Common Denominator.
Least Common Denominator
The least common Denominator (LCD) is the smallest common fraction of two or more Denominators. It is the smallest number that can be the common denominator for the given set of numbers.
To learn more about the least common Denominator (LCD), read the linked article.
For example: let’s solve the fractions with unlike denominators, i.e. 2/5 and 3/6.
2/5 + 3/6 = 12/30 + 15/30 = 12 + 15/30 = 27/30 = 9/10 = 0.9
Multiplication of the Fractions
To solve the multiplication of the fractions, multiply the numerators together and the denominators together.
Example: 3/4 x6/5 = 18/20 = 9/10 = 0.9
Division of the Fractions
To solve the division of the fractions, flip (take the reciprocal of) the second fraction and then multiply.
Example: 8/3 / 8/9 =8/3 x 9/8 = 8 x 9/3 x 8 = 9/3 = 3
Denominators: Solved Questions
1. Solve the given equation: 15/2 + 19/2 – 4/2
Ans. The given equation is 15/2 + 19/2 – 4/2
They have the like denominators, therefore, 15/2 + 19/2 – 4/2 =15 + 19 – 4/2 =30/2 = 15
2. Solve the given equation: 15/5 + 19/5 – 4/5
Ans. The given equation is 15/5 + 19/5 – 4/5
They have the like denominators, therefore, 15/5 + 19/5 – 4/5 =15 + 19 – 4/5 =30/5 = 6
3. Solve the given equation: 15/5 + 3/2
Ans. The given equation is 15/5 + 3/2
They have unlike denominators, therefore, 15/5 + 3/2 =30 + 15/10 =45/10 = 4.5
4. Solve the given equation: 15/5 + 3/10
Ans. The given equation is 15/5 + 3/10
They have unlike denominators, therefore, 15/5 + 3/10 =30 + 3/10 =33/10 = 3.3
5. Solve the given equation: 1/2 + 3/2
Ans. The given equation is 1/2 + 3/2
They have unlike denominators, therefore, 1/2 + 3/2 =1 + 3/2 =4/2 = 2
Denominators: Practice Questions
1. Solve the given equation: 15/8 + 19/9 – 4/2
2. Solve the given equation: 10/7 – 19/2 – 43/2
3. Solve the given equation: 15/13 + 19/17
4. Solve the given equation: 15/6 – 19/7
5. Solve the given equation: 15/18 + 45/19 – 24/21
FAQs on Denominators
What is a denominator?
The denominator is the bottom part of a fraction that indicates the total number of equal parts into which the whole is divided. For example, in the fraction 4/5, 5 is the denominator.
How is the denominator different from the numerator?
The numerator is the top part of a fraction that represents the number of selected parts, while the denominator shows the total number of equal parts that make up the whole.
What does it mean if the denominator is 1?
If the denominator is 1, the fraction represents a whole number. For example, 7/1 = 7.
Why can't a denominator be zero?
A denominator cannot be zero because division by zero is undefined in mathematics. A fraction with a zero denominator does not represent a valid number.
